The geometry of the Qianning-Kangding segment of the Xianshuihe fault zone is quite complex, and it is composed of four secondary-faults, i.e., the Yalahe fault, Selaha-Kangding fault, Zeduotang fault and Moxi fault. On this segment, three strong earthquakes with 34>__7.0 occurred in 1725, 1786 and 1955, respectively. Based on a study of fault landform and geochronology (14C and Thermoluminesense), this paper documents the average horizontal slip rates during the late-Quaternary on all the secondary-faults of the Qianning-Kangding segment as follows: Yalahe fault: (2.0+0.2) ram/a; Selaha-Kangding fault: (5.5+0.6) ram/a; Zeduotang fault: (3.6+0.3) mm/a; Moxi fault: (9.9+0.6) mm/a.The results from the investigation of surface ruptures of historical earthquakes, coseismic-slip and paleo-earthquakes show that the strong-earthquake recurrence intervals are thousands of years on the Yalahe fault, and 230 to 350 years on the Selaha-Kangding and Zeduotang faults. In the next one hundred years, the recurrence of a strong-earthquake on these faults appears impossible. However, the strong-earthquake recurrence interval on the Moxi fault is about 300 years. Up to now, it has been 214 years since the last earthquake (magnitude 7 3/4 ) occurred in 1786, therefore, this fault is now approaching the condition favorable for the next strong earthquake recurrence.